If you are looking for spacious sites, trees, a country setting, and many amenities the place I'm about to recommend won't meet your definition of "nice". It isn't a good place for sitting outside your trailer under the awning. However if you are looking for safe and convenient location in the city where you can easily access any of the many attractions in the Tulsa area this location may fit the bill. It did for us.
We stayed at the RV Park in Expo Square for three nights in the fall of 2013. This is a county park located near downtown. Expo Square has a huge exhibition center and is the site of the Tulsa State Fair. There is also a horse race track with live horse racing.
The RV campsites are on a parking lot. There are three point hookups (water, sewer, and electric). There is a laundry facility in the park office. Pets are allowed on a leash. There is a fence around the camping area. Quiet time 10:00 pm to 7:00 am. Current rate is $40 per night. Sites are very close together, and the campground was nearly full when we were there due to a horse show.
Expo Square is extremely convenient to downtown attractions, Utica Square shopping and restaurants, Philbrook Art Museum, and a short drive to the Gilcrease Museum. Access to the Broken Arrow Expressway is a few blocks away for a quick drive to Broken Arrow.
If we ever return to Tulsa we'll likely stay at Expo Square again instead of finding a campground outside the city.
Here is a link to the web page: Expo Square Tulsa RV Park